Sunday, April 20, 2008

Occam's Razor

I recently engaged a fellow blogger (Orthoprax) in a rather lengthy and tedious argument. I asked him how he knows that God, if He exists, is one. He replied that God is postulated to be singular on the ground of parsimony. He stated that it is a simpler hypothesis to assume that God is one rather than more than one. Needless to say I was unsuccessful in my attempts to convince him otherwise. At one point he called my attempts “annoying” and repetitive.

Nevertheless, I was intrigued by the concept of parsimony or Occam’s Razor. So, I will make another attempt on my blog, where the neighborhood is a bit friendlier.

First, Parsimony, or Occam’s Razor is a logical principle, which states the following:

All else being equal, the simplest hypothesis proposed as an explanation to a given phenomenon is more likely to be the true one among alternate hypotheses.

This is a rather useful principle and is frequently used in scientific thought and in everyday decision making. Let me give some examples:

Suppose you wake up one winter morning and notice that the ground is covered with snow. You wonder what happened at night when you were sleeping. The possibilities are as follows:

It snowed last night and the ground was covered with snow.

A group of professionals with snow making machinery came in when you were sleeping and worked all night to fill the streets with artificial snow.

It started snowing last night, but the snow fall was brief. Following the brief period of snow, the professionals came and augmented the snow with powder.

If you had no other data than the information given to you above, which choice would you consider more likely?

Youmight say that choice #1 is more likely since it only assumes the occurrence of a common and natural process, namely the occurrence of snow in winter time. It is simpler to assume that the ground would be covered by natural snow than man made snow, given that we routinely see natural snow in the winter. You might say that choice #1 is more parsimonious, and thus more likely to be true.

But suppose now that you lived in Southern California. Here, the occurrence of snow is much less common. It is very uncommon to see snow in the Southern California. Perhaps in anticipation of an upcoming motion picture filming, a crew equipped with snow making machinery really made snow to cover your street. Given the information of your location makes possibility 1 and 2 somewhat equally parsimonious. Possibility #3 is not parsimonious since it assumes both snow in a warm climate and existence of machinery. All else being equal, possibility #3 is not parsimonious.

What we learn from the above example are:

Hypotheses which make the least number of assumptions are more likely to be true, all else being the same.

When further information is provided, the parsimony of a given hypothesis is altered.

Now let’s consider one more example:

Suppose I wish to know how many inches of snow are on the ground in place X in the winter. The choices are:

1 inch

2 inches

3 inches

Having no further information, and knowing nothing about place X, can we decide which is the most likely answer? Can we by parsimony argue that choice #1 must be the correct answer since it is the simplest? If not, why not?

Notice here, that the choosing “1 inch” of snow is not any more parsimonious than the other choices.

Let’s see another example:

Last night I went to a party; guess how many people were there:

5

10

20

Here, again, note that we can not give a reasonable guess based simply on parsimony. Any one guess is as good as any other.

Now, one final example:

I own an elaborate watch. How many people have constructed it?

1

5

10

Here, again, notice, that without any further information, we can not guess on the number of people which have made my watch. We can make an educated guess, saying that from what we know usually a team of workers come together to make watches, but this draws from extraneous information. The point is that parsimony does not allow for making this choice.

Now, for the question at hand:

HOW MANY GODS ARE THERE? The choices are:

One

More than one.

I have given an example of how we can use the concept of parsimony to make choices, and I have given examples of circumstances where we can not. Now, to which of these examples does this question belong?

Is it parsimonious to assume that God is one? If so, why?

This fact is that there is no basis to assume that God, if he exists, is one!

Glad to see you blogging here again mr. bad rabbi guy! Thanks for 'approving' of my discussion of hair-covering for women with the lubabich dude, based on a post in your site. I'm glad you enjoyed that.

About G-d vs gods; Don't underestimate that orthoprax guy- deep thinker.. Anyway, I agree with you that it is far from as simple as we often propose (Hindus for example, believe in many gods...if you take it at face value..), but I do think there is some obvious logic in the 'one G-d theory'- namely that it seems to us that it is more likely that primordial matter was put there by only one being, and if he is one, why would he create more gods? To do the work for him while he sits around and watches MTV?!

I enjoyed reading your comments on JP’s site and decided you and DrJ were correct. I decided to stick around but unfortunately, it looks JP’s not having that anymore and is now moderating his blog. All my comments are now being denied posting so keep up the good arguments on his site as I no longer can. I may not be allowed to add my 2 cents anymore but I can read the sane arguments you bring to his nonsense blog. Meanwhile I’m going to keep reading your blog and try to beat him at his own blogging game in other ways.

P.S.- MTV doesn't play music anymore but luckily now the internet does.

Nicely argued BR, and I'm pleased we can continue the conversations over here. Whenever we miss JP too much we you can always link to one his posts and have us go to town on it in your the comments section.

We could also round-table it, and have each of us sceptics agree to defend JP with the expectation that our level of argument must at least surpass that as was provided by natschuster.

:-)

As to the above I was struck immediately that you might have considered a more parsimonious direction to your response to Orthoprax.

If one God is more parsimonious than many Gods, surely no God at all is more parsimonious than Monotheism?

In a general sense the argument is meant to prefer explanations with the fewest 'and then a miracle happens' involved, but in truth while Occam's razor can indicate a reason for preferring one explanation over another, it is not in and of itself a knock-out argument.

For example, String Theory requires a number of extra dimensions, and initially the number speculated went as high as the mid 20's before one of the bigger brained guys collapsed them back down to a more manageable 9.

Parsimony wouldn't have predicted that number would have been required.

So while the razor will suggest we can prefer theories involving fewer entities, it is not a guarantee that.

As to your comment regarding Obama, the fact is he is a politician and the charges you level at him are while probably true, also true of the entire species.

Regarding parsimony and existence of god, I agree that 0 gods are more parsimonious than 1 or more gods. However, for some reason, people seem to think that monotheism is somehow an improvement over polytheism. They think that they have somehow the world has come to recognize that there is only one God. I have been trying to understand why monotheism was a more progressive a philosophy than polytheism. Whatever the reason, parsimony could not be it.

Regarding Obama, I liked the quote that you have on your blog and I agree with the statement. I also agree that politicians are whores by nature. However, I do not like Obama essentially because of his lack of experience and track record, and because it is very difficult to pin him down on his policies. He is a 'feel good' candidate without any apparent substance.

Regarding JP's moderating his comments section, I totally agree with you. I will step up my blogging now that he has proven himself a censorer in addition to being a bad logician. And I totally agree that we should play the round table game as you suggested. My next 2 blogs will be such attempts.

Thanks for your supply of the Chabad link. There, I found the following gem: "By definition, God has no definition"!

Before I respond to the link, I find it ironic that Orthodox Jews (as with all the faithful) require that we pray and worship something that we can not even define. When you raise your heads, arms outstretched, are you praying to something to something that has no definition? By definition, then, you could not be praying to something that could hear you, since if God had the power to hear prayers, necessarily, he could be defined as that which could hear and respond to prayers, which would be giving God a definition!

The depth of logical pitfalls one can fall into when he defines something as undefinable is nothing short of an abyss.

Nevertheless, if you choose to define God as something that has no definition, then OK. If you do so, then necessarily, you could not ascribe the characteristic that He is ONE, any more than you could define him as being TWO, THREE, or even ZERO! God, by definition, is as likely to be 1.2, pi, or an irrational number, or infinity, as he is ONE!

No.Where would one Gd end and the other begin? Would they not step on each other? Who would rule what?

Re the prayers, I don't get your question. Saying that G-d hears our prayers defines him as a "Prayer Listener"? Cmon. We do ascribe certain characteristics and events to Him but that doesn't DEFINE Him.

I do not know. As I understand you, there are no beginnings or endings for a God. But since God supposedly has no definition, who is to say that 2 gods without beginnings or ends can not coexist?

Would they not step on each other?

Your guess is as good as mine. Perhaps, if they are physical entities, they would in fact step into one another's territory. Perhaps they have a pact that they rule certain sectors at certain times. Who knows?

Who would rule what?

Again, your guess is as good as mine. Perhaps a god could concentrate on the Sun, making sure that it produces light. Perhaps one can be a moon god. Maybe another one would be responsible for the rains for the pious farmer.

And perhaps there is only one God responsible for the whole schpazoli. And perhaps there is no god at all.

The point is that there is as much evidence for one god as there is for 2 or more gods.

Two gods, one that rules the sun and one that rules the moon? That's not a god and definitely not a G-D. That would be an angel. G-d directs one angel to rule over the flowers, one over the Chinese, one over broccoli...kacha you could say. But there is ONE ruler over all those angels.

Dude did you read the article or not?? :)

You heard of this-"To know Gd is to be Gd"?

"BTW, why would I not read the article?"I don't know you, haven't read your blog, don't know what kinda guy you are. Many such theological discussions that I've come across are a bunch of ranting confused people who don't want answers. Often, they will not care to delve deeper into what may be a 'solution'. Thus, I was pleasantly surprised that you read it and took it seriously. Then again, as my previous frustration said earlier, i wonder if you internalized it. What final answer are you looking for?

First, your comments are good - you can leave as many of them as you want without risking a spam filter.

Second, I assure you that I read the article you linked, though I am not sure what you meant by "internalized it". I read the article and for reasons that I outlined, I do not agree with it.

Third, it is curious that you say that "by definition, G-d is one", where the very article you link states that God can not be defined! If you want to play the definition games, then I can say the following:

By definition God is pi!

What I am saying is that you can not prove that god is one simply by defining Him as such. You are giving characteristics to entities by fiat or by definitions. It is as if I told you that by definition you have a brother! I have no basis to define this characteristic for you, any more than you can 'define' how many Gods there aught to be. In any case, the Buddhists and other polytheists many not agree with your definition.

What is G-d then? I knew that by saying "By definition, G-d is one" I'd be starting something hehe. My point is that some things cannot be argued about. It's not a matter of me or you figuring it out but rather what it IS.

Please note that the Sun is not hot by definition. Rahter, one of the atributes of the Sun is its temperature. That is, through our scientific understanding, we have come to realize that the sun has very high temperatures. We have not defined it as so.

Similarly, if God has attributes, then we must glean them somehow. We can not willy nilly give attributes to him by definition, and expect them to be true.

In any case, I do not mean to argue the existence of god, as people better than me have done so and at length. I merely attempted to point out in this blog entry that Occam's razor can not be utlized to show that God - if he exists - is one.

i was about to agree with you (re the razor not being able to prove one or two etc) but then i realized that no, it aint true. that can only be applied to say Ghriokians. Can we prove how many Ghirokians there are using Occam's theory? No. We have no idea what Ghirokians are (hint: a species invented right now by the sab) so we cannot know if more than one exist. G-d is not a random word, a freak being.

But ya I don't have the energy for it anymore. I sense a circle-going convo ensuing.

I plowed through The Guide but I must say that much of it was Aristotelian nonsense and I skimmed the last half of it. But if you have read it and know the "very logical explanation" I beg you to share it.

The truth is, the Rambam even discusses why G-D must be one in his Mishna Torah. In the first perek in the seventh halacha he says

"God is not two or more entities, but a single entity of a oneness even more single and unique than any single thing in creation. His oneness is not like that of a single type which consists of many individuals [like the oneness of a species], and nor is it like the oneness of the body, which incorporates many parts, but His oneness is absolutely unique, and there is nothing else in existence with a oneness like His. Had God been more than a single entity, then all of them would have physical bodies, for entities equal in existence differ only in bodily matters. If the Creator did have a body He would have had weaknesses and an end, for it is impossible for a physical body that has no end to exist. The strength of something that has weaknesses and an end also has an end, and a limit. The strength of our God is not like the strength of the body, for it has no end or pause, and perpetually guides the sphere. Since He has no body He has no bodily appearance, and cannot be sub-divided into different parts - therefore, it is impossible for Him to be anything other than one. It is a positive commandment to know this, for it is written, "...the Lord is our God, the Lord is one"."

I give a little bit of an explanation of what is going on here on my blog http://markset565.blogspot.com/2009/02/rambam-singularity-of-g-d-sefer-hamada.html

Basically, once you accept the existence of G-D, it must be that He is one. If you want the exact spot where in the guide he speaks of it, I have to look it up. Also, if you can find the Ralbag on the matter, he is pretty good as well.